# Big Idea Essay

2519 Words Dec 12th, 2012 11 Pages
6: Introduction to Hypothesis Testing
Significance testing is used to help make a judgment about a claim by addressing the question, Can the observed difference be attributed to chance? We break up significance testing into three (or four) steps: Step A: Null and alternative hypotheses The first step of hypothesis testing is to convert the research question into null and alterative hypotheses. We start with the null hypothesis (H0). The null hypothesis is a claim of “no difference.” The opposing hypothesis is the alternative hypothesis (H1). The alternative hypothesis is a claim of “a difference in the population,” and is the hypothesis the researcher often hopes to bolster. It is important to keep in mind that the null and alternative
If P ≤ α, we will reject the null hypothesis. Otherwise it will be retained for want of evidence.

Page 6.1 (C:\data\StatPrimer\hyp-test.doc Last printed 7/13/2006 10:59:00 PM)

One-Sample z Test
The one-sample z test is used to compare a mean from a single sample to an expected “norm.” The norm for the test comes from a hypothetical value or observations in prior studies, and does not come from the current data. In addition, this test is used only when the population standard deviation σ is known from a prior source. Finally, data represent a SRS, and measurements that comprise the data are assumed to be accurate and meaningful. Example (“Lake Wobegon”). Garrison Keller claims the children of Lake Wobegon are above average. You take a simple random sample of 9 children from Lake Wobegon and measure their intelligence with a Wechsler test and find the following scores: {116, 128, 125, 119, 89, 99, 105, 116, and 118}. The mean of this sample ( x ) is 112.8. We know Wechsler scores are scaled to be Normally distributed with a mean of 100 and standard deviation of 15. Is this sample mean sufficiently different from a population mean µ of 100 to reject the null hypothesis of “no difference?” The null and alternative hypotheses The claim being made in the illustrative example is that the population has

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